Rational inattention in control of Markov chains

Shafieepoorfard, Ehsan

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https://hdl.handle.net/2142/72985 Copy

Description

Title

Rational inattention in control of Markov chains

Author(s)

Shafieepoorfard, Ehsan

Issue Date

2015-01-21

Director of Research (if dissertation) or Advisor (if thesis)

Raginsky, Maxim

Department of Study

Electrical & Computer Eng

Discipline

Electrical & Computer Engr

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

M.S.

Degree Level

Thesis

Date of Ingest

2015-01-21T19:55:22Z

Keyword(s)

• Markov Chain
• Information Theory
• Control
• Limited capacity
• Optimization

Abstract

This thesis poses a general model for optimal control subject to information constraint, motivated in part by recent work on information-constrained decision-making by economic agents. In the average-cost optimal control framework, the general model introduced in this paper reduces to a variant of the linear-programming representation of the average-cost optimal control problem, subject to an additional mutual information constraint on the randomized stationary policy. The resulting in nite-dimensional convex program admits a decomposition based on the Bellman error, which is the subject of study in approximate dynamic programming. Later, we apply the general theory to an information-constrained variant of the scalar Linear-Quadratic-Gaussian (LQG) control problem. We give an upper bound on the optimal steady-state value of the quadratic performance objective and present explicit constructions of controllers that achieve this bound. We show that the obvious certainty-equivalent control policy is suboptimal when the information constraints are very severe, and propose another policy that performs better in this low-information regime. In the two extreme cases of no information (open-loop) and perfect information, these two policies coincide with the optimum.

Graduation Semester

2014-12

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http://hdl.handle.net/2142/72985

Copyright and License Information

Copyright 2014 Ehsan Shafieepoorfard

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